A simple variance estimator for the trapezoidal area-under-the-curve estimator of the spawner abundance of Pacific salmon

Abstract

The trapezoidal area-under-the-curve (TAUC) method is the simplest and most widely used method for estimating the spawning abundance of Pacific salmon from periodic surveys of spawner counts within a surveyed area. However, there is currently no method to estimate the precision of the estimated spawner abundance from the survey data. For this reason the Gaussian area-under-the-curve (GAUC) method was recently presented as an easily implemented alternative that has the advantage of having a variance estimator. However, under a diverse variety of simulation scenarios, the TAUC estimator was seen to be a slightly better estimator of escapement on the basis of mean squared error. It is shown here that a variance estimator for the TAUC method can be obtained as an immediate by-product of the GAUC method. Furthermore, this new approach can easily be extended to accommodate asymmetric and multimodal patterns of spawner abundance by the use of basis splines.